{"paper":{"title":"A Structural Characterization of the Hit Image in the Motivic Steenrod Algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Dang Vo Phuc","submitted_at":"2026-01-27T12:26:09Z","abstract_excerpt":"The motivic hit problem seeks a minimal set of generators for $H^{*,*}(BV_n; \\mathbb{F}_{2})$ as a module over the mod $2$ motivic Steenrod algebra. Kameko demonstrated the failure of the motivic Peterson conjecture by constructing non-hit monomials $z_k$ in degree $d = k + 2d_1$. His analysis involves a distinguished summand in the quotient $N_n = M_n / (\\tau)$ spanned by monotone translates of $z_k$. In this paper, we isolate the local top-layer content of this summand before quotienting by hit elements. We construct a linear projection $\\vartheta: N_n^{d,*} \\longrightarrow V$ onto the $M_1$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.00118","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.00118/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}